Question

(√ c-7√ d)(c+7√ cd+49d)-(√ c+7√ d)(c-7√ cd+49d)

Answer 1

$( \sqrt{c} -7 \sqrt{d})(c+7 \sqrt{cd}+49d)-(\sqrt{c} +7 \sqrt{d})(c-7 \sqrt{cd}+49d)= \\\ =(c^{1.5}-343d^{1.5})-(c^{1.5}+343d^{1.5})=c^{1.5}-343d^{1.5}-c^{1.5}-343d^{1.5} \\\ =-686d^{1.5}$

Answer 2

$(\sqrt{c}-7\sqrt{d})(c+7\sqrt{cd}+49d)-(\sqrt{c}+7\sqrt{d})(c-7\sqrt{cd}+49d)=\\=(\sqrt{c}-7\sqrt{d})((\sqrt{c}+7\sqrt{d})^2-7\sqrt{cd})-\\-(\sqrt{c}+7\sqrt{d})((\sqrt{c}-7\sqrt{d})^2+7\sqrt{cd})=\\=7\sqrt{cd}(7\sqrt{d}-\sqrt{c}-\sqrt{c}-7\sqrt{d})=-14\sqrt{cd}(\sqrt{c})=-14c\sqrt{d}$

Answer 3

To simplify the given expression:

(√c - 7√d)(c + 7√cd + 49d) - (√c + 7√d)(c - 7√cd + 49d)

First, expand each term in the expression:

= (√c * c + √c * 7√cd + √c * 49d - 7√d * c - 7√d * 7√cd - 7√d * 49d) - (√c * c - √c * 7√cd - √c * 49d + 7√d * c - 7√d * 7√cd + 7√d * 49d)

Now, simplify the expression:

= (√c * c cancels with -√c * c) + (√c * 7√cd cancels with -√c * 7√cd) + (√c * 49d cancels with -√c * 49d) + (-7√d * c cancels with 7√d * c) + (-7√d * 7√cd cancels with 7√d * 7√cd) + (-7√d * 49d cancels with 7√d * 49d)

= 0

So, the simplified expression is 0.